Effects of paramagnetic cations on the nonexponential spin-lattice relaxation of rare spin nuclei in solids

Nonexponential spin-lattice relaxation is often observed for rare spin nuclei in the solid state. Deviation from single-component decay may be amplified by the coupling of rare spin nuclei to paramagnetic centers. Nonexponential spin-lattice relaxation was observed in derivatized silica gels resins. This phenomenon was localized and enhanced when paramagnetic transition metal cations were bound to surface functional groups. A stretched exponential analysis method was determined to be robust in fitting nonexponential relaxation curves for silica gels both with and without bound paramagnetic ions. Spin-lattice relaxation rates (T₁⁻¹) for functional group nuclei increased as a function of percent surface coverage with metal ion. The magnitude of the relaxation rate increase was dependent upon internuclear distances from the paramagnetic center. At low surface coverages, a semi-random distribution of paramagnetic centers increased the degree of stretching of spin-lattice relaxation decays, as measured by decreases in the calculated stretching parameter β. At higher surface coverages, calculated β values reached a limiting value, indicating that while the spin-diffusion mechanism in metal-ex-changed silica gels is restricted, it is not completely diminished.     

A multi-frequency EPR spectroscopy approach in the detection of boson peak excitations

The influence of boson peak (BP) excitations on low-temperature spin-lattice relaxation rate of a paramagnetic center embedded in a glassy matrix is investigated in the context of multi-frequency electron paramagnetic resonance (EPR) detection. In the theoretical analysis, the transition rate of spin one-half in the presence of a phonon field is calculated within the approximation of Fermi's golden rule. Several phonon densities of states are compared, among which one originating from a model of quasi-localized vibrations has been introduced into electron spin relaxation formalism for the first time. The respective frequency dependencies of spin-lattice relaxation rates are predicted which should lead to observable effects of BP modes if a multi-frequency study at very low temperatures is performed.     

Distance between a native cofactor and a spin label in the reaction centre of Rhodobacter sphaeroides by a two-frequency pulsed electron paramagnetic resonance method and molecular dynamics simulations

The distance between the paramagnetic state of a native cofactor and a spin label is measured in the photosynthetic reaction centre from the bacterium Rhodobacter sphaeroides R26. A two-frequency pulsed electron paramagnetic resonance method [double-electron-electron spin resonance (DEER)] is used. A distance of 3.05 nm between the semiquinone anion state of the primary acceptor (Q(A)) and the spin label at the native cysteine at position 156 in the H-subunit is found. Molecular-dynamics (MD) simulations are performed to interpret the distance. A 6 ns run comprising the entire RC protein yields a distance distribution that is close to the experimental one. The average distance found by the MD simulation is smaller than the distance obtained by DEER by at least 0.2 nm. To better represent the experiments performed at low temperature (60K), a MD method to mimic the freezing-in of the room-temperature conformations is introduced. Both MD methods yield similar distances, but the second method has a trend towards a wider distance distribution.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Single-crystal (57)Fe Q-band ENDOR study of the 4 iron-4 sulfur cluster in its reduced [4Fe-4S](1+) state.

(57)Fe Q-band ENDOR has been used to study the [4Fe-4S](1+) state created by gamma irradiation of single crystals of the synthetic model compound [N(C(2)H(5))(4)](2)[Fe(4)S(4)(SCH(2)C(6)H(5))(4)] enriched in (57)Fe. This compound is an excellent biomimetic model of the active sites of many 4 iron-4 sulfur proteins, enabling detailed and systematic studies of its oxidized [4Fe-4S](3+) and reduced [4Fe-4S](1+) paramagnetic states. Taking advantage of the fact that Q-band ENDOR, in contrast with X-Band ENDOR, allows for a very good separation of the (57)Fe transitions from those of the protons, the complete hyperfine tensors of the four iron atoms for the [4Fe-4S](1+) species has been measured with precision. For each iron atom, the electron orbital and electron spin isotropic contributions have been determined separately. Moreover, it is remarkable that two (57)Fe hyperfine tensors attributed to the ferrous pair of iron atoms are very different. In effect, one tensor presents a much larger anisotropic part and a much smaller isotropic part than those of the other. This difference has been interpreted in terms of a differential electron orbital hyperfine interaction among the two ferrous ions.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation at 4.7 T and 300 K due to fixed paramagnetic nitrogen defects

13C spin-lattice relaxation times in the laboratory frame, ranging from 1.4 to 36 h, have been measured on a suite of five natural type Ia and Ib diamonds at 4.7 T and 300 K. Each of the diamonds contains two types of fixed paramagnetic centers with overlapping inhomogeneous electron paramagnetic resonance (EPR) lines. EPR techniques have been employed to identify these defects and to determine their concentrations and relaxation times at X-band. Spin-lattice relaxation behavior of 13C in diamonds containing paramagnetic P1, P2, N2. and N3 centers are discussed. Depending on the paramagnetic impurity types and concentrations present in each diamond, three different nuclear spin-lattice relaxation (SLR) paths exist, namely that due to electron SLR mechanisms and two types of three-spin processes (TSPs). The one three-spin process (TSP1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a flip of a 13C spin, while the other process (TSP2) involves two electron spins belonging to different hyperfine EPR lines and a 13C spin. It is shown that the thermal contact between the 13C nuclear Zeeman and electron dipole-dipole interaction reservoirs is field dependent, thus forming a bottleneck in the 13C relaxation path due to TSP1 at high magnetic fields.     

Electron spin-relaxation via vibronic level of nickel (I) and nickel (III) cyanide complexes in NaCl single crystals

Electron spin-lattice relaxation rates for the low spin [Ni(CN)(4)](1-) and [Ni(CN)(4)](3-) complexes in NaCl host lattice were measured by the inversion recovery technique in the temperature range 7-50K. The data for both paramagnetic species fit very well to a relaxation process involving localized anharmonic vibration modes, also responsible for the g-tensor temperature dependence.     

Nuclear spin resonance of (129)Xe doped with O(2)

Spin-lattice relaxation of (129)Xe nuclei in solid natural xenon has been investigated in detail over a large range of paramagnetic O(2) impurity concentrations. Direct measurements of the ground state magnetic properties of the O(2) are difficult because the ESR (electron spin resonance) lines of O(2) are rather unstructured, but NMR measurements in the liquid helium temperature region (1.4-4 K) are very sensitive to the effective magnetic moments associated with the spin 1 Zeeman levels of the O(2) molecules and to the O(2) magnetic relaxation. From these measurements, the value of the D[Sz(2)-(1/3)S(2)] spin-Hamiltonian term of the triplet spin ground state of O(2) can be determined. The temperature and magnetic field dependence of the measured paramagnetic O(2)-induced excess line width of the (129)Xe NMR signal agree well with the theoretical model with the spin-Hamiltonian D=0.19 meV (2.3 K), and with the reasonable assumption that the E[S(x)(2)-S(y)(2)] spin-Hamiltonian term is close to 0 meV. An anomalous temperature dependence between 1.4 K and 4.2K of the (129)Xe spin-lattice relaxation rate, T(1n)(-1)(T), is also accounted for by our model. Using an independent determination of the true O(2) concentration in the Xe-O(2) solid, the effective spin lattice relaxation time (which will be seen to be transition dependent) of the O(2) at 2.3 K and 0.96 T is determined to be approximately 1.4 x 10(-8)s. The experimental results, taken together with the relaxation model, suggest routes for bringing highly spin-polarized (129)Xe from the low temperature condensed phase to higher temperatures without excessive depolarization.     

A study of the thermal contact between the nuclear Zeeman system and the electron dipole-dipole interaction system

In order to explain proton spin-lattice relaxation measurements in a deuterated copper Tutton salt [1], we performed a theoretical investigation of the thermal contact between the proton Zeeman system (PZS) and the electron dipole-dipole interaction system (EDDS). The basic process that maintains the contact between these two spin systems is a three-spin process in which one proton spin and two electron spins make a simultaneous transition. We calculated the transition probability of this three-spin process. It was proved that neither electron spin-lattice relaxation nor cross-relaxation are a bottle-neck in the proton spin-lattice relaxation, so the observed relaxation time values are completely determined by this three-spin process. Hence, the contact time between the PZS and the EDDS can be derived directly from the measurements.     

Nuclear magnetic relaxation by regularly distributed dense paramagnetic ions in a quasi-two-dimensional system

The ¹H nuclear spin-lattice relaxation behavior was characterized in the perovskite-type layered structure quasi-two-dimensional Heisenberg paramagnets, (C_nH_2n+1NH₃)₂MnCl₄,with different chain lengths (n=8, 10, and 12). In contrast to the case of the short-chain compound with n=8, the nuclear spin diffusion to the electron spin system alone is not able to fully account for the spin-lattice relaxation in the compounds with longer chain lengths. Our results are discussed in light of the nuclear magnetic relaxation by the regularly distributed dense paramagnetic ions.     

Spin coupling in iron proteins and model complexes

Transition metal ions are essential for the specific function of many biomolecules, like transport and activation of small molecules, electron transfer, etc. Their active sites contain (i) single paramagnetic or diamagnctic metal ions, or (ii) clusters of spin-coupled paramagnetic centers. Examples are for (i) hemoglobin or rubredoxin with one Fe, and for (ii) ferredoxins with [2Fe-2S] and [4Fe-4S] clusters, cytochrome c oxidasc containing Fe and Cu, or peroxidases with metal-radical pairs. Here, we present the results of our Mössbauer and EPR investigation of irondioxygen interaction in horse liver alcohol dehydrogenase (HLADH), of ironradical interaction in synthetic analogues of heme peroxidases and of iron-iron double exchange interaction in a synthetic ferric/ferrous mixed valence complex. We hope to demonstrate that the understanding of spin coupling can yield valuable insight in the relation between electronic structure and function of biological iron complexes.

     

Longitudinal muon spin relaxation in muonium-like systems

Nuclear spin-lattice relaxation in paramagnetic systems is treated using the classic expression for transition probability between the coupled electron and nuclear spin states. The rate equations governing the incoherent occupancies of these states are solved analytically (where possible) and numerically (where not) to construct the relaxation function for the nuclear spin. The method is illustrated for muonium, and the muonium-substituted molecular radicals, for the case of perturbation due to fluctuation of the local field,i.e. modulation of the interaction with a third spin. A slight departure from single exponential behaviour is demonstrated for slow fluctuations.     

Electron spin relaxation by spin-rotation interaction in benzoyl and other acyl type radicals

In various studies of the spin dynamics in radical pairs, benzoyl-type radicals have been one of the two paramagnetic pair species. Their electron spin relaxation has been assumed to be slow enough to be neglected in the data analysis. This assumption is checked by measuring the electron spin relaxation in a sequence of three acyl radicals (benzoyl, 2,4,6-trimethylbenzoyl and hexahydrobenzoyl) by time-resolved electron paramagnetic resonance spectroscopy. In contrast to the assumed slow relaxation, rather short spin-lattice relaxation times (100–400 ns) are found for benzoyl and 2,4,6-trimethylbenzoyl radicals from the decay of the integral initial electron polarization to thermal equilibrium at different temperatures and viscosities. The relaxation is induced by a spin-rotation coupling arising from two different types of radical movements: overall rotation of the whole radical and hindered internal rotation of the CO group. The predominant second contribution depends on the barrier of the internal rotation. The obtained results are well explained in the frame of Bull’s theory when using a modified rotational correlation time τ _J . The size of the spin-rotation coupling due to the internal CO group rotation in benzoyl radicals is estimated to be |C _α|=1510 MHz.     

Comparing continuous wave progressive saturation EPR and time domain saturation recovery EPR over the entire motional range of nitroxide spin labels

The measurement of spin-lattice relaxation rates from spin labels, such as nitroxides, in the presence and absence of spin relaxants provides information that is useful for determining biomolecular properties such as nucleic acid dynamics and the interaction of proteins with membranes. We compare X-band continuous wave (CW) and pulsed or time domain (TD) EPR methods for obtaining spin-lattice relaxation rates of spin labels across the entire range of rotational motion to which relaxation rates are sensitive. Model nitroxides and spin-labeled biological species are used to illustrate the potential complications that arise in extracting relaxation data under conditions typical to biological experiments. The effect of super hyperfine (SHF) structure is investigated for both CW and TD spectra. First and second harmonic absorption and dispersion CW spectra of the nitroxide spin label, TEMPOL, are all fit simultaneously to a model of SHF structure over a range of microwave amplitudes. The CW spectra are novel because all harmonics and microwave phases were acquired simultaneously using our homebuilt CW/TD spectrometer. The effect of the SHF structure on the pulsed free induction decay (FID) and pulsed saturation recovery spectrum is shown for both protonated and deuterated TEMPOL. We present novel pulsed saturation recovery measurements on biological molecules, including spin-lattice relaxation rates of spin-labeled proteins and spin-labeled double-stranded DNA. The impact of structure and dynamics on relaxation rates are discussed in the context of each of these examples. Collisional relaxation rates with oxygen and transition metal paramagnetic relaxants are extracted using both continuous wave and time domain methods. The extent of the errors inherent in the CW method and the advantages of pulsed methods for unambiguously measuring collisional relaxation rates are discussed. Spin-lattice relaxation rates, determined by both CW and pulsed methods, are used to determine the electrostatic potential on the surface of a protein.     

Long-range ferromagnetic dipolar ordering of high-spin molecular clusters

We report the first example of a transition to long-range magnetic order in a purely dipolarly interacting molecular magnet. For the magnetic cluster compound Mn6O4Br4(Et2dbm)6, the anisotropy experienced by the total spin S = 12 of each cluster is so small that spin-lattice relaxation remains fast down to the lowest temperatures, thus enabling dipolar order to occur within experimental times at T(c) = 0.16 K. In high magnetic fields, the relaxation rate becomes drastically reduced and the interplay between nuclear- and electron-spin lattice relaxation is revealed.     

Features of low-frequency spin dynamics in manganite LaMnO3 according to 139La NMR data

The spin-lattice and spin-spin relaxation times of ¹³⁹La are measured in manganite LaMnO₃. Analysis of the frequency dependence of the spin-lattice relaxation rate in the paramagnetic temperature range shows that this quantity is determined by magnetic fluctuations. The magnitude of the fluctuating field is estimated. It is shown that the correlation time for spin fluctuations varies with temperature in accordance with the Arrhenius law. The high value of the spin-spin relaxation rate in the paramagnetic region can be due to strong anisotropy of fluctuating magnetic fields at La nuclei.     

19F nuclear spin relaxation and spin diffusion effects in the single-ion magnet LiYF4:Ho3+

Temperature and magnetic field dependences of the ¹⁹F nuclear spin-lattice relaxation in a single crystal of LiYF₄ doped with holmium are described by an approach based on a detailed consideration of the magnetic dipole-dipole interactions between nuclei and impurity paramagnetic ions and nuclear spin diffusion processes. The observed non-exponential long time recovery of the nuclear magnetization after saturation at intermediate temperatures is in agreement with predictions of the spin-diffusion theory in a case of the diffusion limited relaxation. At avoided level crossings in the spectrum of electron-nuclear states of Ho^{3 +} ions, rates of nuclear spin-lattice relaxation increase due to quasi-resonant energy exchange between nuclei and paramagnetic ions in contrast to the predominant role played by electronic cross-relaxation processes in the low-frequency ac-susceptibility.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Four complementary theoretical approaches for the analysis of NMR paramagnetic relaxation

Four theoretical and computational approaches used at the University of Michigan to analyze NMR paramagnetic relaxation enhancement (NMR-PRE) are described. The primary objective of the theory is to describe the relationship of the NMR-PRE phenomenon to the electron spin hamiltonian and the spin energy level structure when zero field splitting interactions are significant. Four formulations of theory are discussed: (1) spin dynamics simulation; (2) the laboratory frame "constant H(S)" formulation; (3) the Molecular Frame "constant H(S)" formulation; and (4) the zfs-limit "constant H(S)" formulation. No single theoretical approach describes all important aspects of the relaxation mechanism in a fully satisfactory way. We use the four formulations in a complementary manner to provide as complete a picture of the relaxation mechanism as possible. We also discuss the integration of NMR-PRE theory and recently developed theory of electron spin relaxation which accounts for effects of the permanent zfs hamiltonian.